The head of each executive department and constitutional agency and in the case of the judicial branch of the government the chief justice of the supreme court, and in the case of the legislative branch of the government the president pro tem of the senate and the speaker of the house of representatives acting together, shall exercise the option to insure or self-insure in the best interest of the state and shall perform such duties as may be necessary or incidental to carry out effectively the purposes of sections 105.800 to 105.850.